Strong decays of the hidden-charm molecular pentaquarks

We investigate the strong decays of the recently observed hidden-charm pentaquarks $P_{\psi}^N(4312)$, $P_{\psi}^N(4440)$, and $P_{\psi}^N(4457)$, as well as $P_{\psi s}^\Lambda(4338)$ and $P_{\psi s}^\Lambda(4459)$, within the molecular framework using the effective Lagrangian approach. We construct the effective Lagrangians describing the S-wave couplings between these pentaquarks and their constituent hadrons, namely $\Sigma_c\bar{D}^{(*)}$ and $\Xi_c\bar{D}^{(*)}$, and determine the coupling constants via the residues of the scattering $T$-matrix at the bound-state poles. Our results show that the decay widths are sensitive to the cutoff parameters in the form factors, whereas the branching fractions exhibit only weak dependence. Using $P_{\psi}^N(4312)$ to calibrate the cutoff range, we further explore the spin assignments of $P_{\psi}^N(4440)$ and $P_{\psi}^N(4457)$. Our calculations favor the assignment where the lower-mass state $P_{\psi}^N(4440)$ carries higher spin $J = 3/2$ and the higher-mass state $P_{\psi}^N(4457)$ carries lower spin $J = 1/2$. In addition, the experimental widths of $P_{\psi s}^\Lambda(4338)$ and $P_{\psi s}^\Lambda(4459)$ can both be well reproduced under the molecular interpretation. We look forward to future experimental analyses with more accumulated data to clarify whether the lineshape of $P_{\psi s}^\Lambda(4459)$ contains contributions from both spin-$1/2$ and spin-$3/2$ states.